11 November 2017

Simplified Measurements

As units of weights and measures have evolved in the course of time, each subdivision had their own specific use, each trade their own measurement. Food stuff were measured in pounds because a pound of potatoes, for example, is just how much one eats in a few days. Precious metals and medications were measured in ounces, because an ounce of silver could be a week's wage worth for a worker. An acre is the land surface one can plow with a horse in roughly a day. Two hundred square foot is the size of a comfortable family kitchen (at times when it was the only heated room in the house and families did not much space).
As there was no much need to mix those different domains of life, there was also no pressure to force all measurements into a single system.
However, with the advent of science and technology there were more and more connections between all the different things. How many pills can be made from a pound of base material? How many family homes can be build on one acre?

This is just a very brief glimpse on the motivation behind introducing a decimal system where number conversions simply happen by shifting the comma. (Once the decimal system was used in a majority of places, many others followed not for its intrinsic practicality, but just to ease international trade.)

But what about time?

So now most of the world measures weights as 1 ton = 1'000 kg = 1'000'000 grams and lengths in meters with set of prefixes which in daily life go from 1 km = 1'000 m = 100'000 cm = 1'000'000 mm and in specialist industries can go much further up and down. Of the three physical base units, weight and space and time, however, time has escaped decimalization. It even has escaped twice, once with the small units of time which come in packs of 60 and 24, and even more radically on the calendrical level where the subdivisions are not only chaotic like having on one hand 52 weeks of 7 days, on the other hand 12 months of 28 to 31 days and years of either 365 or 366 days that need to be broken up! Now, we're looking at very different kinds of problems when trying to sort this out: on the one hand, days and years are given to us by the universe and each correspond to a different amount of time that does not provide an integer subdivision. When we think of "ending the year" on midnight December 31st, this is a calendrical illusion because the Earth will not be exactly at the same point around the sun as it was at the same time exactly 365 or 366 days before. This is a problem that we have to solve with good conventions and we can do so with some liberty because no human will notice the seasons shifting for a small number of days as long as those small numbers don't add up over the years.

The other problem, however, is caused by the completely human set intervals of weeks and months which only increase the irregularity instead of decreasing it. Without even thinking of introducing decimal 10-day weeks like the French Revolution did (and the Soviet Revolution tried it again), let's look at the issues that are actually solvable:

Saying how many weekdays (working days) and how many weekend days are in any given year with not more than one extra bit of information. Today you need to know which year it is or at least with which day of week it starts and whether it is a leap year. In a simple calendar the answer should only depend on the leap year bit and optimally also not differ too much.

Saying how many workdays and non-workdays are in each month and each quarter.

Then, answer the above questions also taking public holidays into account which may or may not fall on a weekend, reducing the number of workdays only if they don't.

Saying how many days or weeks there are between two different dates in the same year or of a different year.

Saying what day of the week a specific day will we.

Currently, answer to the counting questions are: 5*52 plus zero, one, or two, that is, 260, 261, or 262 workdays per year, and 104, 105, or 106 weekend days per year. With public holidays it depends on the country and region (and sometimes, the city).

For a quarter, there are currently 90, 91, or 92 days where two difference days can again be either weekends or workdays, so the relative uncertainty is even bigger.

A Simplified Calendar does not need change radically

Now, the surprise I want to explain here is that we can already simplify those questions and more by making two small changes to the current calendar! There is no need to change all months to be exactly 4 weeks long (thus getting 13 months per year and killing the concept of a quarter-year) and also no need to change any of the month's lengths at all except for the placement of the leap day (which is currently February 29th) and breaking of a two-thousand year old dogma.

Let's start with the easier of the two and make good use of the fact that the 52 weeks in a year very neatly fall in 4 packs of 13. So a quarter-year as used by most business for accounting purposes could always have 13 full weeks and therefore a fixed number of 65 working days and 26 weekend days. In the Gregorian Calendar as we use it today, starting a quarter at the first day of January, April, July, and October, the length of the quarters is 92 in Q3 and Q4, 91 in Q2, and 90 or 91 in Q1 depending on it being a leap year or common year. So if we moved the leap day to Q3 or Q4 then each quarter would have 91 or 92 days, which means there will always be at least 13 full weeks plus optionally an extra day. If we could arrange for that extra day to always fall on a weekend, we would even get four quarters with exactly 65 working days and 26 or 27 non-working days! And all of that with a change that still keeps all the 366 dates of the Gregorian Calendar. (Only that February 29th will be there every year and some other day in Q3 or Q4 will only exists in leap years.)

Now, did you get suspicious when you read the phrase "arrange for that extra day to always fall on a weekend" above? Any given date (that is month plus day-in-month) can of course fall on any day of the week. For example, Gregorian leap year 2012 had the very nice property of starting the first, second, and third quarter on a Sunday. And the common year 2017 had the nice property that the first and last quarter started with a Sunday while the year also ended with a Sunday. If we just took the calendars for those years and put them together we'd get a year in which each quarter starts with a Sunday and ends (if it has 91 days) on a Saturday, or if it has 92 days on a Sunday. This would automatically mean that the quarters all have exactly 65 working days! Ain't that great?!

Do you see the problem yet? All quarters starting on a Sunday and ending on a Saturday means that the last day of each quarter, a Saturday, will be followed by the first day of the next quarter, a Sunday, which is what happend to all Saturdays in the 2000 year history of the Gregorian and Julian calendars! However, for those quarters which end in a Sunday, the next day –oh dogma!– would again be a Sunday so that each quarter can indeed start its rhythm in the same, fixed scheme. Note that I just chose Sunday for the sake of example, because it seemed practical to have an extra week-end day. If it seems less blasphemous to my reader, we can repeat the same argument with the common year 2016 and a suitably chosen leap year both starting on a Saturday and then get one or two extra Saturdays per year. We could also just call them Leap Day or Extra-Weekend-Day. Or give them any other name as if we were creating a public holiday.

As a side note: an average Gregorian year has 365.2425 * 5/7 = 260.8875 work days whereas the regular calendar described here always has only 260 working days. So that's almost one extra public holiday. (Since all other public holidays will now fall on fixed days of the week, governments will probably want to recount the net sum of public holidays on work days and shift some of those around, so that this additional day could also be dedicated to some higher meaning.)

If you can hold the idea of having one extra long weekend every year (and two in leap years) then we can think a little about where in the year those extra long weekends should be! In fact, by suggesting that we simply repeat one of the good Gregorian years every year, I already arrived at the conclusion that the first and last day of the year would be the same day of the week, so there's an obvious place to put that extra long week-end: as in most countries 1st January is already a public holiday and 31st December is a big party. Of course that party would be easier to organize if it were on a weekend and that's exactly what we'll achieve! During a time where many people take vacation anyways, this does not interrupt the flow of society and rather helps people save up their vacation days for other times of the year.

From what I wrote above, it is also clear that the other long week-end should be placed in the third quarter (July, August, or September). Since it is a leap day which will not be there in all of the years, it should be the last day of any of those months. Since with the proposed scheme of starting and ending the year and all quarters on week-ends, only the end of September is on a week-end, September 30th suggests itself as the leap day.

To sum up how this regularized calendar looks like:

All months keep their existing length, but February 29th is in every year and September, 30th is only in leap years.

The first days of each quarter, that is 1st of January, April, July, and October, as well as the last days of September and December will be a Sunday (or if you like that variant: a Saturday).

Each business quarter will have exactly 65 working days and 13 weekends with usually two days. All quarters start at the same day of the week.

The weekend which spans the new year has three days. (Either because December 31st and January 1st are the same day of the week or because December 31st is a special day of the week.)

In leap years, the weekend around September 30st also has three days.

Every date has the same day of week and week-number in every year. So if someone needs to make day-of-week calculations even easier, they can always switch between a week-based date (Q1, week 6, Monday) and a month-based date, because the conversion is the same in every year.

Years are the same as Gregorian into the past and into the future. Dates between the new leap day (Sept 30th) and the old leap day (Feb 29th) are also the same in all years. Other dates only differ by one day and only in common years.

If you like all of this, you might also be interested to know:

how would this calendar actually look like on paper or in your calendar app?

what would change about the plan if Feb 29th stayed as leap day (so that all dates would still be equivalent with Gregorian days in all years)? Could we arrange for Feb 29th to fall on a weekend and place the other extra day such that it does not disrupt the usual flow of work and non-work days? Could we then still achieve a fixed number of working days per quarter? (Having a four-day week or an only one-day weekend in all common years just doesn't sound as attractive as an occasional three-day weekend.)

what would be some really cool names to give to those non-septemiary extra days of the week?

what would be a practical arrangement of holidays in your country in the proposed regular calendar which keeps a regular distribution of working days in each quarter? (Maybe follow the Canadian example of spreading the public holidays such that there is more or less one in every month.)